Bayern, playing in their seventh straight Champions League quarter-final, never needed to hit top form but were in control throughout with the largely toothless Spaniards only rarely venturing into their opponents' box.
The Germans, who last won the treble in 2013 again under coach Jupp Heynckes, had secured a 2-1 advantage from last week's first leg and advanced after having been eliminated by a Spanish team in each of the past four seasons.
Sevilla ended the game with ten men after the dismissal in stoppage time of Joaquin Correa for a rough challenge on Javi Martinez.
The result, however, meant Sevilla, in the last eight of the European Cup for the first time since their only previous appearance at this stage 60 years ago, still managed to snap Heynckes' 12-game record winning run in the competition.
"Sevilla have a good team and they proved it," Bayern winger Arjen Robben told reporters. "But we had enough chances and we should have scored. Defensively everything has to work in the Champions League and it did for us tonight.
"In the Champions League you always have to bring your top performance and we will need to improve, that's clear."
In a physical first half Bayern, fresh from securing the Bundesliga title last weekend, were by far the more dangerous team with Robert Lewandowski and Franck Ribery coming close.
Poland forward Lewandowski, who was sporting a swollen eye after some robust defending, also narrowly headed wide four minutes after the restart.
Sevilla at times looked to be lacking a sense of urgency and were badly let down by their final pass, stumbling time and again at the edge of the box and failing to get a shot on target in the entire first half.
"We are a bit upset," said Sevilla captain Sergio Escudero. "We came here, tried, believed in the comeback but it was not to be.
"In the first half, we had chances. Maybe we could have scored and changed the tie. We go home upset."
They did hit the bar with a Correa header on the hour and Ever Banega fired narrowly wide a little later as they upped the pressure briefly in search of the two goals they needed.
As Sevilla ran out of ideas, the match ended with a touch of uproar as Correa was shown a straight red card for a poor and late challenge on Martinez.
Bayern, though, having won 20 of their last 21 Champions League matches at home going into the game, could once again celebrate a familiar last-four ticket with a degree of comfort.
(Reporting by Karolos Grohmann; Editing by Ian Chadband)
